Question

Triangle a'b'c' is result of dilating abc about point a by a scale factor of 4/3. Determine whether each claim about the properties of abc and a'b'c' is true or false

Answer 1

Dilating triangle ABC by a factor of 4/3 about point A produces a similar triangle A'B'C' with sides 4/3 times the original, preserving angles but changing the area.

Step-by-step explanation:

The properties of triangles after a dilation transformation. In geometry, when a triangle ABC is dilated about a point A by a scale factor of 4/3, the new triangle A'B'C' will have sides that are 4/3 times the length of the corresponding sides of the original triangle ABC.

This process preserves the angles, making the two triangles similar. However, areas of similar triangles are not equal but rather are scaled by the square of the scale factor. This concept is derived from the basic geometric principles of similar triangles and the Pythagorean theorem where a² + b² = c² helps to determine the relationship between the sides of a right-angled triangle.

Answer 2

True , because all properties preserved under dilation from triangle abc to a'b'c'.

Given : A triangle abc is dilated by a factor of 2/3 , result triangle a'b'c'

To find :After dilation, properties of triangle abc and a'b'c' is true or false.

Dilation of a triangle are result either decrease or increase the corresponding length of triangle , its depends on by which scale factor triangle is dilated ,and dilation does not affect the angle measures of triangle.here scale factor is 2/3 so corresponding sides of triangle a'b'c' decreases. So, dilation of triangle are not congruent but similar to the original triangle abc